Subdividing a simple plane does not work
You have subdivided the edges and not the faces. If you go to vertex selection and zoom in into one of the edges, you will see many many unnecessary vertices. To fix this, just select your corner vertices (change to vertex selection, pressing Ctrl+Tab), Shift+RMB  the corner vertices, then press Ctrl+I to inverse selection, press X and delect all the unnecessary vertices.
Press a until corner vertices are selected and press F to fill. Then Ctrl+Tab to face selection, then you can subdivide the faces.
If it crashes, by the amount of vertices built, you may to this, select just the corner vertices, press P and seperate by selection.
Exit the edit mode, delete the old object (that has huge amount of vtx), go to your new object  that has just the desired vtx, select all by pressing a, press F, change to face selection, subdivide.